<div style="margin: 12px 0px; font-family: arial; color: #333333; background: #ffffff; border: solid 4px #e5e5e5; width: 100%; clear: left;"><div class="CM_CTB_Content_Wrap" style="margin: 0px; padding: 0px;background-color: #ffffff;"><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content.clipmarks.com/blog_embed/be264bea-4190-4148-9f7f-e0d2c7ceeaeb/7C121AFE-A9AB-4AC0-998B-6A3187FB6608/" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory" href="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory" style="font-size: 11px;">www.sciencenews.org</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory"><DIV class="topic content_description print"> Unknotting knot theory </DIV></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory">October 31st, 200</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory"><DIV class="content_authors print"> By <A href="http://www.sciencenews.org/view/authored/id/43/name/Julie_Rehmeyer" class="anonymous print">Julie Rehmeyer</A></DIV></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory"><DIV class="content_summary print">New techniques are beginning to unravel the mysteries of knots, revealing a great mathematical superstructure in the process</DIV></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory">One of the reasons knots have given mathematicians fits is that the same knot can appear in very different guises. Tug here, tug there, and soon a knot will become unrecognizable, but remain fundamentally unchanged. To allow a knotted string to wiggle around without danger of untying, mathematicians seal its two ends together, making it a knotted circle. The first question mathematicians have to answer is simply, when are two knots really, secretly the same?</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory">Alexander polynomial</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory">1983, Vaughn Jones of the University of California, Berkeley</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory"> 1988, physicist Edward Witten of the Institute for Advanced Study in Princeton turned Jones’ single invariant into a whole zoo of new invariants </blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory">Jones and Witten the Fields medal, one of the highest honors in mathematics, in 1990</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory">Khovanov homology</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory">knot Floer homology</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/38237/title/Unknotting_knot_theory">Sergei Gukov</blockquote></div><div style="margin: 0px 6px 6px 4px;"><table style="font-size: 11px;border-spacing: 0px;padding: 0px;" cellpadding="0" cellspacing="0" width="100%"><tr><td style="background:transparent;border-width:0px;padding:0px;">&nbsp;</td><td align="right" style="background:transparent;border-width:0px;padding:0px;width:107px" width="107"><a href="http://clipmarks.com/share/7C121AFE-A9AB-4AC0-998B-6A3187FB6608/blog/" title="blog or email this clip"><img src="http://content9.clipmarks.com/images/c2b-foot.png" border="0" alt="blog it" width="107" height="17" style="border-width:0px;padding:0px;margin:0px;" /></a></td></tr></table></div></div>

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